{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "view-in-github"
   },
   "source": [
    "# Analysis"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 37
    },
    "id": "El49NgachrYj",
    "outputId": "867cd0cc-78dd-470c-c8d6-6b55d9daa8dd"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'1.8.1+cu102'"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import torch\n",
    "torch.__version__"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "id": "Dumky9Ut1vHJ"
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import torch\n",
    "import torch.distributions as td\n",
    "import matplotlib.pyplot as plt\n",
    "import torch.nn as nn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "from collections import namedtuple, OrderedDict, defaultdict\n",
    "from tqdm.auto import tqdm\n",
    "from itertools import chain\n",
    "from tabulate import tabulate\n",
    "import pickle"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "import sys\n",
    "sys.path.append(\"../\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "from pathlib import Path"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "id": "WDWb-ohmPxy_"
   },
   "outputs": [],
   "source": [
    "from components import GenerativeModel, InferenceModel, VAE\n",
    "from data import load_mnist\n",
    "from hparams import load_cfg, make_args\n",
    "from main import make_state, get_batcher, validate"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "from analysis import compare_marginals, compare_samples"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Load model and data\n",
    "\n",
    "* Load hyperparameters\n",
    "* Load model state\n",
    "* Load MNIST data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "num_samples = 100"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Overriding device to user choice cuda:1\n",
      "Overriding data_dir to user choice ../tmp\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Config(seed=14, batch_size=100, data_dir='../tmp', height=28, width=28, output_dir='trained_models/dirichlet//jumping-bee-20', device='cuda:1', y_dim=0, z_dim=10, prior_z='dirichlet 1.0', hidden_dec_size=500, posterior_z='dirichlet 1e-3 1e3', hidden_enc_size=500, epochs=500, num_samples=100, gen_opt='adam', gen_lr=0.001, gen_l2=0.0, gen_p_drop=0.0, inf_opt='adam', inf_lr=0.001, inf_p_drop=0.0, inf_l2=1e-06, grad_clip=5.0, wandb_freq=10, project='iclr-submission', tqdm=False, cfg='cfg/iclr-dirichlet.json', prior_f='gibbs 0.0', prior_y='dirichlet 1.0', posterior_f='gibbs -10 10', posterior_y='dirichlet 1e-3 1e3', shared_enc_fy=True, mean_field=True, training_samples=1, lr_warmup=0, load_ckpt=None, reset_opt=False, exact_marginal=False, exact_KL_Y=False, use_self_critic=False, use_reward_standardisation=False, ppo_like_steps=0, gsp_cdf_samples=100, gsp_KL_samples=1)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model_type = 'dirichlet'\n",
    "experiment = 'jumping-bee-20'\n",
    "directory = f'../trained_models/{model_type}/{experiment}/'\n",
    "args = make_args(\n",
    "    load_cfg(\n",
    "        f\"{directory}/cfg.json\", \n",
    "        # use this to specify a decide for analysis\n",
    "        device='cuda:1',\n",
    "        # use this to change paths if you need\n",
    "        data_dir='../tmp',\n",
    "    )\n",
    ")\n",
    "args"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "PosixPath('pdfplots/dirichlet/jumping-bee-20')"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plots_dir = Path(f\"pdfplots/{model_type}/{experiment}\")\n",
    "plots_dir"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "plots_dir.mkdir(parents=True, exist_ok=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'cuda:1'"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "args.device"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "state = make_state(\n",
    "    args, \n",
    "    device=args.device, \n",
    "    # change this to .best if you want the best ckpt (rather than the last)\n",
    "    ckpt_path=f\"{directory}/ckpt.last\"\n",
    "    #ckpt_path=f\"{directory}/training.ckpt\"\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 845,
     "referenced_widgets": [
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      "32dde89004e541a78ee6d35af5d3f14b",
      "05389b71a6b545cf9b61d9f63f79c894",
      "642b9f5fb1624f2c97344e8e7a6c5d20",
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      "9328008d582947ee9a7dddef3d6571da",
      "f839264c20cd46feb8ce184e87e85416",
      "8be95b95873544a79de9124a8ed267d8",
      "09a30ad3b16444309a2f2591382c5735"
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    },
    "id": "lymJpzWjiAr2",
    "outputId": "346ad792-2d1a-45ca-a6ca-4a4cb59c5e3f"
   },
   "outputs": [],
   "source": [
    "train_loader, valid_loader, test_loader = load_mnist(\n",
    "    args.batch_size, \n",
    "    save_to=args.data_dir, \n",
    "    height=args.height, \n",
    "    width=args.width\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's check the validation results:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "ebc971baf1814bc6a221f19a983aa48f",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "  0%|          | 0/50 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saved ckpt - Validation: nll=94.63 bpd=13.65\n"
     ]
    }
   ],
   "source": [
    "val_metrics = validate(state.vae, get_batcher(valid_loader, args), 1000, progressbar=True, compute_DR=True)\n",
    "print(f'Saved ckpt - Validation: nll={val_metrics[0]:.2f} bpd={val_metrics[1]:.2f}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Samples from prior"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here we draw some sampels from the generative model (via the prior) and anlyse the results. \n",
    "\n",
    "To help do it systematically, we use a KNN classifier trained on MNIST. This classifier achieves F1=95% on MNIST test set."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "knn_model = pickle.load(open('knnclassifier.pickle', 'rb'))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "from analysis import collect_samples"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First, we gather samples:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "prior, _ = collect_samples(\n",
    "    state.vae, \n",
    "    get_batcher(valid_loader, args), \n",
    "    args, \n",
    "    num_samples=1, \n",
    "    data_sample=True,\n",
    "    from_prior=True,\n",
    "    from_posterior=False,\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(5000, 784)"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x_gen_prior = np.concatenate(prior['x'])\n",
    "x_gen_prior.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Then, we classify the model samples using a KNN classifier trained on (actual) MNIST."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "knn_pred = knn_model.predict(x_gen_prior)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "clustered = defaultdict(list)\n",
    "for x_, y_ in zip(x_gen_prior, knn_pred):\n",
    "    clustered[y_].append(x_)\n",
    "clustered = {cls: np.stack(digits) for cls, digits in clustered.items()}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "p_emp = np.array([len(clustered.get(c, []))/x_gen_prior.shape[0] for c in range(10)])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's check a grid of plots with model samples grouped by predicted class:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x720 with 100 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axs = plt.subplots(\n",
    "    10, 10, \n",
    "    figsize=(15, 10),\n",
    "    sharex=True, sharey=True,\n",
    "    gridspec_kw={'hspace': 0, 'wspace': 0},\n",
    ")\n",
    "for c in range(10):\n",
    "    axs[c, 0].imshow(clustered.get(c, np.zeros((1, 28 * 28))).mean(0).reshape(args.height, args.width), cmap='Greys')    \n",
    "    for i, k in enumerate(np.random.choice(len(clustered.get(c, [])), size=9)):\n",
    "        axs[c, i + 1].imshow(clustered[c][k].reshape(args.height, args.width), cmap='Greys')\n",
    "\n",
    "for ax in axs.flat:\n",
    "    ax.set_xticks([])\n",
    "    ax.set_yticks([])\n",
    "#_ = fig.suptitle(r'Samples from prior clustered by KNN classifier with F1=95%')\n",
    "fig.savefig(plots_dir / 'prior-grid.pdf', bbox_inches='tight')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's group the model samples by predicted class and inspect a single 'marginal' plot per class:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 10 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axs = plt.subplots(\n",
    "    2, 5, \n",
    "    sharex=True, sharey=True,\n",
    "    gridspec_kw={'hspace': 0, 'wspace': 0})\n",
    "for c in range(10):\n",
    "    axs[c // 5, c % 5].imshow(clustered.get(c, np.zeros((1, 28 * 28))).mean(0).reshape(args.height, args.width), cmap='Greys')\n",
    "    axs[c // 5, c % 5].set_xlabel(f\"({c}) {p_emp[c] * 100:.2f}\") #set_title(f\"X'|X={c}\")\n",
    "for ax in axs.flat:\n",
    "    ax.set_xticks([])\n",
    "    ax.set_yticks([])\n",
    "# Hide x labels and tick labels for top plots and y ticks for right plots.\n",
    "#for ax in axs.flat:\n",
    "#    ax.label_outer()\n",
    "#_ = fig.suptitle(r'Samples from prior clustered by KNN classifier with F1=95%')\n",
    "fig.savefig(plots_dir / 'prior-marginal.pdf', bbox_inches='tight')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "dz90e7lyzOwe"
   },
   "source": [
    "# Training Curves"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "id": "1BiQHIBHwJrr"
   },
   "outputs": [],
   "source": [
    "np_stats_tr = {k: np.array(v) for k, v in state.stats_tr.items()}\n",
    "np_stats_val = {k: np.array(v) for k, v in state.stats_val.items()}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "def smooth(v, kernel_size=100):\n",
    "    if kernel_size is None:\n",
    "        return v\n",
    "    return np.convolve(v, np.ones(kernel_size)/kernel_size, 'valid')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 1000
    },
    "id": "-y3TFeJgwrbv",
    "outputId": "f6c5d3d2-0ea0-4e1b-f309-938be21c2d44",
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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QfoKbmVl3a+ZWGy0l6e2S1lS9XpJ0ac08syS9WDXP59tdTzOzbtfMdRAtFRFPANPgjVt5bAGWZ2b9UUSc08aqmZlZlbb3IGq8D3gyIjaVXA8zM6tRdkDMA5bVmXaGpAcl3SbpxHorkLRQUp+kvv7+/mJqaWbWhUoLCEn7A79L5R5PtR4Ajo2Ik4G/A26qt56IWBIRvRHR29PTU0hdzcy6UZk9iLOAByJiW+2EiHgpIl5Jw7cC+0ma2O4Kmpl1szIDYj51di9JOlKS0vAMKvV8ro11MzPrem0/iwlA0sHA+4FPVpVdCBAR1wLnAZ+StBN4DZgXEb7/k5lZG5USEBHxKnB4Tdm1VcNXA1e3u15mZrZb2WcxmZnZCOWAMDOzLAeEmZllOSDMzCzLAWFmZlkOCDMzy3JAmJlZlgPCzMyyHBBmZpblgDAzsywHhJmZZTkgzMwsywFhZmZZDggzM8tyQJiZWZYDwszMshwQZmaWVVpASNoo6WFJayT1ZaZL0t9KWi/pIUnTy6inmVm3KuWRo1XeGxHP1pl2FjA1vU4DrknvZmbWBiN5F9O5wNej4l5gvKRJZVfKzKxblBkQAdwhabWkhZnpRwFPVY1vTmV7kLRQUp+kvv7+/oKqambWfcoMiJkRMZ3KrqSLJJ05lJVExJKI6I2I3p6entbW0Mysi5UWEBGxJb1vB5YDM2pm2QIcUzV+dCozM7M2KCUgJB0s6dCBYWA2sLZmtpuB89PZTKcDL0bE1jZX1cysa5V1FtMRwHJJA3X4ZkTcLulCgIi4FrgVmAusB34OfKykupqZdaVSAiIiNgAnZ8qvrRoO4KJ21svMzHYbyae5mplZiRwQZmaW5YAwM7MsB4SZmWU5IMzMLMsBYWZmWQ4IMzPLckCYmVmWA8LMzLIcEGZmluWAMDOzLAeEmZllOSDMzCzLAWFmZlkOCDMzy3JAmJlZlgPCzMyy2h4Qko6R9ANJj0p6RNIlmXlmSXpR0pr0+ny762lm1u3KeOToTuDTEfGApEOB1ZJWRsSjNfP9KCLOKaF+ZmZGCT2IiNgaEQ+k4ZeBx4Cj2l0PMzNrrNRjEJKmAKcAqzKTz5D0oKTbJJ3YYB0LJfVJ6uvv7y+qqmZmXae0gJB0CPBd4NKIeKlm8gPAsRFxMvB3wE311hMRSyKiNyJ6e3p6CquvmVm3KSUgJO1HJRxuiIgba6dHxEsR8UoavhXYT9LENlfTzKyrlXEWk4DrgMci4kt15jkyzYekGVTq+Vz7amlmZmWcxfRu4I+AhyWtSWWfBSYDRMS1wHnApyTtBF4D5kVElFBXM7Ou1faAiIh7AO1jnquBq9tTIzMzy/GV1GZmltX1AVHblWnYtTEz6yJdHxBj1HjczKxbdX1A7IrG42Zm3arrA6I2D5wPZmYVXR8QZmaW54AwM7MsB4SZmWU5IMzMLMsBYWZmWV0fEG/ab0zDcTOzbtX1v4bnnzGl4biZWbcq426uI8qiue8A4PZHnmHOiUe+MW5m1u3USXfR7u3tjb6+vrKrYWY2akhaHRG9uWldv4vJzMzyHBBmZpblgDAzsywHhJmZZTkgzMwsywFhZmZZHXWaq6R+YNMQF58IPNvC6owkndw26Oz2uW2j12hp37ER0ZOb0FEBMRyS+uqdCzzadXLboLPb57aNXp3QPu9iMjOzLAeEmZllOSB2W1J2BQrUyW2Dzm6f2zZ6jfr2+RiEmZlluQdhZmZZDggzM8vq+oCQNEfSE5LWS1pUdn0akbRR0sOS1kjqS2WHSVopaV16n5DKJelvU7sekjS9aj0L0vzrJC2oKj81rX99WlYFt2eppO2S1laVFd6eettoQ9uukLQlfX5rJM2tmnZZqucTkj5QVZ79fko6TtKqVP5tSfun8gPS+Po0fUoBbTtG0g8kPSrpEUmXpPJR/9k1aFtHfHaDFhFd+wLGAk8CxwP7Aw8CJ5Rdrwb13QhMrCn7H8CiNLwI+O9peC5wGyDgdGBVKj8M2JDeJ6ThCWnafWlepWXPKrg9ZwLTgbXtbE+9bbShbVcAn8nMe0L67h0AHJe+k2MbfT+B7wDz0vC1wKfS8J8A16bhecC3C2jbJGB6Gj4U+Flqw6j/7Bq0rSM+u0H/e5RdgVIbD2cAK6rGLwMuK7teDeq7kb0D4glgUhqeBDyRhr8CzK+dD5gPfKWq/CupbBLweFX5HvMV2KYp7PkjWnh76m2jDW2r9yOzx/cOWJG+m9nvZ/rRfBYYV/s9Hlg2DY9L86ngz/B7wPs76bPLtK0jP7t9vbp9F9NRwFNV45tT2UgVwB2SVktamMqOiIitafgZ4Ig0XK9tjco3Z8rbrR3tqbeNdrg47WZZWrV7ZLBtOxx4ISJ21pTvsa40/cU0fyHSbpBTgFV02GdX0zbosM+uGd0eEKPNzIiYDpwFXCTpzOqJUfnTo2POW25He9r8b3YN8FZgGrAVuKpN2y2EpEOA7wKXRsRL1dNG+2eXaVtHfXbN6vaA2AIcUzV+dCobkSJiS3rfDiwHZgDbJE0CSO/b0+z12tao/OhMebu1oz31tlGoiNgWEa9HxC7gq1Q+Pxh8254DxksaV1O+x7rS9Den+VtK0n5UfkBviIgbU3FHfHa5tnXSZzcY3R4Q9wNT01kF+1M5MHRzyXXKknSwpEMHhoHZwFoq9R04+2MBlX2mpPLz0xkkpwMvpq75CmC2pAmpmzybyj7QrcBLkk5PZ4ycX7WudmpHe+pto1ADP2zJB6l8fgP1mZfOYjkOmErlIG32+5n+cv4BcF6mDdVtOw/4v2n+VrZDwHXAYxHxpapJo/6zq9e2TvnsBq3MAyAj4UXlDIufUTnj4HNl16dBPY+ncibEg8AjA3Wlso/yTmAd8C/AYalcwN+ndj0M9Fat6+PA+vT6WFV5L5Uv/pPA1RR/cHMZle76v1PZF3tBO9pTbxttaNs3Ut0fovJjMKlq/s+lej5B1dlj9b6f6ftwX2rzPwMHpPID0/j6NP34Ato2k8qunYeANek1txM+uwZt64jPbrAv32rDzMyyun0Xk5mZ1eGAMDOzLAeEmZllOSDMzCzLAWFmZlkOCLMMST9J71MkfbTF6/5sbltmI41PczVrQNIsKjdpO2cQy4yL3ffayU1/JSIOaUH1zArlHoRZhqRX0uBi4D3pGQD/UdJYSV+UdH+6cdsn0/yzJP1I0s3Ao6nspnRjxUcGbq4oaTFwUFrfDdXbSlcaf1HSWlWehfCRqnXfJel/S3pc0g3pil+zQo3b9yxmXW0RVT2I9EP/YkS8S9IBwI8l3ZHmnQ6cFBH/msY/HhE7JB0E3C/puxGxSNLFETEts63fp3IzuJOBiWmZu9O0U4ATgaeBHwPvBu5pdWPNqrkHYTY4s6ncV2gNldtAH07l/jsA91WFA8CfSXoQuJfKTdim0thMYFlUbgq3Dfgh8K6qdW+Oys3i1lB51oRZodyDMBscAX8aESv2KKwcq3i1Zvx3qDwA5ueS7qJyr52h+mXV8Ov4/661gXsQZo29TOXRkwNWAJ9Kt4RG0tvS3XVrvRl4PoXDb1B5fOaAfx9YvsaPgI+k4xw9VB5bel9LWmE2BP4rxKyxh4DX066i64H/RWX3zgPpQHE/8HuZ5W4HLpT0GJW7fN5bNW0J8JCkByLiD6rKl1N5BOWDVO4o+ucR8UwKGLO282muZmaW5V1MZmaW5YAwM7MsB4SZmWU5IMzMLMsBYWZmWQ4IMzPLckCYmVnW/wc0u85ifTva+gAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "for k, v in np_stats_tr.items():\n",
    "    v = smooth(v)\n",
    "    plt.plot(np.arange(1, v.size + 1), v, '.')    \n",
    "    plt.ylabel(f'Training {k}')\n",
    "    plt.xlabel('iteration')\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "FY26XI0FzUm8"
   },
   "source": [
    "# Validation Curves"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "metric        mean       min\n",
      "--------  --------  --------\n",
      "val_nll    95.1727   94.9547\n",
      "val_bpd    13.7305   13.6991\n",
      "val_ELBO  -99.1215  -99.7246\n",
      "val_D      79.2324   78.9106\n",
      "val_R      19.889    19.7042\n",
      "val_R_Z    19.889    19.7042\n"
     ]
    }
   ],
   "source": [
    "print(tabulate(\n",
    "    [(k, np.mean(v[-100:]), np.min(v[-100:])) for k, v in np_stats_val.items()],\n",
    "    headers=['metric', 'mean', 'min']\n",
    "))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 541
    },
    "id": "XoLBOF45yivl",
    "outputId": "d1fa5183-3cec-428c-d8d2-cb2bf72cd44f",
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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uAO4n6WK6MCJGKn9yfXgdg5nZWLkSg6SVJL/gjwZ+AJwF/IRk4du4IuK8CsVfq3L95cDleWKql9HJoTTw7ORgZq0q75YY7wBeD/w6Is4HXkVys54ZrzRldWBwiOD5Katez2BmrSpvYhiKiD3Ac+mitx1kB4pnLE9ZNTPLyjvG0CepE/gqyWK3P1DgwrNG8pRVM7OsWusYvgh8MyLelxZ9WdIPgRdFxD2FR9cAnrJqZpZVqyvp58A/SnpY0j9IWhIRD8+WpACVt94WcPrL5zUnIDOzJqu1JcbnIuIU4HXA74DVkh6UtFLSyxoSYcGWLeni7a/uQmVlAXxn44AHoM2sJeUafI6IRyLi0xGxBDiP5H4MDxQZWCPd+uBORu+r4QFoM2tVuRKDpH0kvVnSGpJN7/qBtxUaWQN5ANrM7Hm1Bp//lKSFcDbJ9hTXAcsj4pkGxNYwHoA2M3terRZDL/CfwCsi4i0R8c3ZlhQgGYBun6NMWfscec8kM2tJtTbRm9TuqTOSahybmbWIvCufZ7VVG/oZHskOPw+PhAefzawlOTHgwWczs3JODIw/yOzBZzNrRU4MePWzmVk5Jwa8+tnMrJwTQ8qrn83MEk4MKQ9Am5klnBhSHoA2M0sUmhgkrZa0Q9K9ZWV/Juk+SXsk9Yy6vlfSVkn9kpYWGdto4w00ewDazFpN0S2Gq4EzR5XdS7IB3+3lhZKOBs4Fjknf8yVJbTTIrQ/urFh+492PNyoEM7NpodDEEBG3A0+MKnsgIiqN6J4DXBcRuyPiV8BW4MQi4ys33ljC4NCwZyaZWUuZTmMMXcBjZcfb0rIxJC2X1Cepb+fOyn/pT1S1sYTL1t9Xl+8wM5sJplNiyC0iroqInojomTevPmMA1XZSdavBzFrJdEoMA8CCsuPD07KGWLaki4P3bx/3vNczmFmrmE6JYT1wrqT9JB0JLCa5OVDDrHzzMeOe83oGM2sVRU9XvRb4KdAtaZukCyS9VdI24BTg+5I2AETEfcANwP3AD4ELI2KkyPhGW7aki/3bK/+TvGCccjOz2abqjXqmKiLOG+fUd8e5/nLg8uIiqm2/9jZ2De8ZUz40vId1mwZYtqTieLiZ2azhP4NHGdw1PO45jzOYWStwYhil2rTVAY8zmFkLcGIYpdq0VcDTVs1s1nNiGKXWGMKKb9/t5GBms5oTQwVdVbqThkfCYw1mNqs5MVRQqzvJYw1mNps5MVRQaxU0wDu/+tMGRWNm1lhODOOotgoa4D8eesLJwcxmJSeGceRpNfzHQ094INrMZh0nhipWvvkYVOOa3rX3NCQWM7NGcWKoYtmSLt558sKq1wwN76H70n9zy8HMZg0nhho+sexYTn3JIVWv2f3cHi6+fjOXrtvSoKjMzIrjxJDDmveewn771P6n+sYdjzo5mNmM58SQ06ffflyu675xx6PuVjKzGc2JIadlS7p4V43xhpKLr9/Mko//yAnCzGYkJ4YJyDPeUPLkrmEuvn4zx3z0h04QZjajODFM0Jr3nsIB+7blvv6ZZ0c8MG1mM4oTwyRc/tZj6WjPnxwgGXtw68HMZgJFRLNjmJKenp7o6+tr+Peu2zTAZevvY3Bo/Du+VXPw/u2sfPMxvlWomTWFpI0R0VPpXKEtBkmrJe2QdG9Z2SGSbpL0i/T54LRckj4vaaukeySdUGRsU7VsSRebV74h95jDaKUxiEWXfN8D1WY2rRTdlXQ1cOaoskuAmyNiMXBzegxwFrA4fSwHriw4trpY895Tcs9WGo+ThJlNJ4V3JUlaBNwYEa9Mj/uB0yLicUmHAf8eEd2SvpK+vnb0ddU+v1ldSZWs2zRA79p7GBreM+XPOmDfNnY9O8L8zg5WLO12l5OZ1VXTupLGcWjZL/tfA4emr7uAx8qu25aWzRjLlnTxwN+fNeUWBCSzmYLkpkCe9mpmjbRPM788IkLShJsskpaTdDexcOHUfwnX2yeWHUvPEYfUrfUAz097vfj6zXvLPIBtZkVwV1LB6tm9VM0cwV+etJBPLDu20O8xs9mhWldSM1oM64H3AJ9Kn79XVn6RpOuAk4CnaiWFmWDZkq69f9Ffum4L37jj0UK+Z08kayWqfb5bGGaWR6EtBknXAqcBc4HfACuBdcANwELgEeDPI+IJSQK+QDKLaRdwfkTUbApM9xbDaFNd/1BvThZmralai8EL3Jpk3aYBVm3oZ/vgEAd1tPP7oWGK7Wyamv3b57BfexuDu4Y9U8psFnBimCGK7GoqUpsgSLqzypWSyZO7hmmTGImgy0nFbFpwYpiBpluXU6PMUZJgujo7OP3l87j1wZ1sHxxyK8WszpwYZpFGzXKaLUYvFAQyCddjLNaqnBhmodIYxcDgULNDsdT+7cl60V1lSbs88Vy6bgvX/uwxRiJokzjvpAUVpxeXjz+5pWRFcWJoMeVJQyT9/2ZT0T4HqjVSSwkQGNMFevD+7bzxuMO48e7HK3aNlifPiSbF0ZM4JBjcNZx57eRamRODAa07bmE2HR2wbxvPPDsyqfd21iHxTbcFbtYk5YvtKilvaZRmEZlZMSabFIDMH3cDg0P0rk3uEFmvVpETg+1VK3GUc+vDbPoYGh5h1YZ+JwZrrokkkUqcWMzqa3sdJ6I4MVhTTLR1Mt6AZKVzfY88wZo7HvWgu7WU+Z0ddfssDz6b5TC6hVNtFo5Zowm44i+On1Ar3oPPZlNUrYUzE6ZB1poGmnddzL5tYp85yqzVsOZ758kL6/pz6BaDmU1LeZNZ6Xy1LVQmcm21zx+9FmOO4JSjDuGuRwf37kZQujdKzxGHjFlj8eSufC3LSvuMVVqTdMC+bVz+1mMnlRS8jsHMzDKm2z2fzcxsGnNiMDOzDCcGMzPLcGIwM7MMJwYzM8uY8bOSJO0EHpnk2+cCv61jODOB69waXOfWMJU6HxER8yqdmPGJYSok9Y03XWu2cp1bg+vcGoqqs7uSzMwsw4nBzMwyWj0xXNXsAJrAdW4NrnNrKKTOLT3GYGZmY7V6i8HMzEZxYjAzs4yWTAySzpTUL2mrpEuaHU+9SFotaYeke8vKDpF0k6RfpM8Hp+WS9Pn03+AeSSc0L/LJk7RA0q2S7pd0n6QPpuWztt6SXiDpTkl3p3X+WFp+pKSfpXW7XtK+afl+6fHW9PyiplZgCiS1Sdok6cb0eFbXWdLDkrZI2iypLy0r/Ge75RKDpDbgi8BZwNHAeZKObm5UdXM1cOaoskuAmyNiMXBzegxJ/Renj+XAlQ2Ksd6eA/4uIo4GTgYuTP97zuZ67wbOiIhXAccDZ0o6Gfg0cEVEvBR4Erggvf4C4Mm0/Ir0upnqg8ADZcetUOfTI+L4svUKxf9sR0RLPYBTgA1lx71Ab7PjqmP9FgH3lh33A4elrw8D+tPXXwHOq3TdTH4A3wP+tFXqDewP3AWcRLICdp+0fO/PObABOCV9vU96nZod+yTqenj6i/AM4EaSO1rO9jo/DMwdVVb4z3bLtRiALuCxsuNtadlsdWhEPJ6+/jVwaPp61v07pN0FS4CfMcvrnXapbAZ2ADcBDwGDEfFcekl5vfbWOT3/FPBHDQ24Pv4J+BBQuq/oHzH76xzAjyRtlLQ8LSv8Z9v3fG4hERGSZuX8ZEkHAt8BLo6I30vae2421jsiRoDjJXUC3wVe3tyIiiXpTcCOiNgo6bQmh9NIfxIRA5JeDNwk6cHyk0X9bLdii2EAWFB2fHhaNlv9RtJhAOnzjrR81vw7SGonSQprImJtWjzr6w0QEYPArSTdKJ2SSn/slddrb53T8wcBv2tspFN2KvAWSQ8D15F0J32O2V1nImIgfd5B8gfAiTTgZ7sVE8N/AYvT2Qz7AucC65scU5HWA+9JX7+HpA++VP7udCbDycBTZc3TGUNJ0+BrwAMR8dmyU7O23pLmpS0FJHWQjKk8QJIg3pFeNrrOpX+LdwC3RNoJPVNERG9EHB4Ri0j+n70lIt7JLK6zpAMkvbD0GngDcC+N+Nlu9uBKkwZ0zgZ+TtIv++Fmx1PHel0LPA4Mk/QvXkDSr3oz8Avgx8Ah6bUimZ31ELAF6Gl2/JOs85+Q9MPeA2xOH2fP5noDxwGb0jrfC3w0LT8KuBPYCnwL2C8tf0F6vDU9f1Sz6zDF+p8G3Djb65zW7e70cV/pd1Ujfra9JYaZmWW0YleSmZlV4cRgZmYZTgxmZpbhxGBmZhlODGZmluHEYNZEkk4r7RRqNl04MZiZWYYTg1kOkt6V3gNhs6SvpJvY/UHSFek9EW6WNC+99nhJd6R74n+3bL/8l0r6cXofhbskvST9+AMlfVvSg5LWqHyjJ7MmcGIwq0HSK4C/AE6NiOOBEeCdwAFAX0QcA9wGrEzfcg3wvyLiOJIVqKXyNcAXI7mPwn8jWaUOyY6wF5PcH+Qokn2BzJrGu6ua1fZ64NXAf6V/zHeQbFy2B7g+veYbwFpJBwGdEXFbWv514FvpnjddEfFdgIj4fwDp590ZEdvS480k99T4SeG1MhuHE4NZbQK+HhG9mULpI6Oum+z+MrvLXo/g/y+tydyVZFbbzcA70j3xS/fcPYLk/5/Szp5/CfwkIp4CnpT02rT8r4DbIuJpYJukZeln7Cdp/0ZWwiwv/2ViVkNE3C/pUpI7ac0h2b32QuAZ4MT03A6ScQhItkL+cvqL/5fA+Wn5XwFfkfTx9DP+rIHVMMvNu6uaTZKkP0TEgc2Ow6ze3JVkZmYZbjGYmVmGWwxmZpbhxGBmZhlODGZmluHEYGZmGU4MZmaW8f8BE+GZjLHbncgAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "for k, v in np_stats_val.items():\n",
    "    plt.plot(np.arange(1, v.size + 1), v, 'o')\n",
    "    plt.ylabel(f'Validation {k}')\n",
    "    plt.xlabel('epoch')\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "metric        mean      std\n",
      "--------  --------  -------\n",
      "IS-NLL     94.6348\n",
      "IS-BPD     13.6529\n",
      "ELBO      -99.5102  34.2121\n",
      "D          79.3766  29.1797\n",
      "R          20.1336  14.8637\n",
      "R_Z        20.1336  14.8637\n"
     ]
    }
   ],
   "source": [
    "rows = [('IS-NLL', val_metrics[0], None), ('IS-BPD', val_metrics[1], None)]\n",
    "val_DR = val_metrics[2]\n",
    "for k, v in val_DR.items():\n",
    "    rows.append((k, v.mean(), v.std()))\n",
    "print(tabulate(rows, headers=['metric', 'mean', 'std']))    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "_ = plt.hist(val_DR['D'], bins='auto')\n",
    "_ = plt.xlabel('D')\n",
    "plt.show()\n",
    "\n",
    "_ = plt.hist(val_DR['R'], bins='auto')\n",
    "_ = plt.xlabel('R')\n",
    "plt.show()\n",
    "\n",
    "if state.vae.p.z_dim:\n",
    "    _ = plt.hist(val_DR['R_Z'], bins='auto')\n",
    "    _ = plt.xlabel('R(Z)')\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "ndBexD8IzXDi"
   },
   "source": [
    "# Analysis"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It's good to check that the aggregated posterior is reasonably close to the prior, when this is not the case, we might need to check the VAE. It's not obvious what might cause such a thing, but it could be due to local optimality, which in turn may be due to too noisy gradient estimates. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "import torch_two_sample as t2s\n",
    "from analysis import collect_samples"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "prior, posterior = collect_samples(state.vae, get_batcher(valid_loader, args), args, num_samples=100)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "When thing we can do is to check a test statistics, such as MMD, low values indicate the two samples are closer, though note MMD cannot be used to 'accept' the null hypothesis (that the two samples come from the same distribution). Take this as just a sanity check, not as a certificate. \n",
    "\n",
    "It's unclear what hyperparameters to use, so we compute the MMD statistic over a range of values and plot the distribution of results:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "for rv, dim in [('z', state.p.z_dim)]:\n",
    "    if dim == 0:\n",
    "        continue\n",
    "    p_f = np.stack(prior[rv]).reshape(-1, dim)\n",
    "    q_f = np.stack(posterior[rv]).reshape(-1, dim)\n",
    "    mmd = t2s.statistics_diff.MMDStatistic(p_f.shape[0], q_f.shape[0])\n",
    "    v = np.array([mmd(torch.tensor(p_f), torch.tensor(q_f), [alpha]).cpu().numpy() for alpha in np.random.gamma(10., 1./10, size=20)])\n",
    "\n",
    "    _ = plt.hist(v, color='blue', alpha=0.3, label='')\n",
    "    _ = plt.axvline(x=v.mean(), c='blue')\n",
    "    _ = plt.xlabel(f\"MMD {rv}\")\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## KL"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 1000
    },
    "id": "DasiABbHu5mc",
    "outputId": "4259154c-0094-4078-ff1c-896c02b9680e",
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "For a trained VAE: \n",
      " 1. We want to see that KL(Z|x || Z), KL(F|x || F), and KL(Y|f,x || Y|f) are generally > 0 for any x ~ D.\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " 2. But, marginally, we expect E_X[Z|X] ~ Z E_X[F|X] ~ F and E_FX[Y|F,X] ~ E_F[Y|F].\n"
     ]
    },
    {
     "data": {
      "image/png": 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KGgNWj90lfc28mXWjDFDUKAt9zrz39TxoOW5UXc/XKXIMABQ1Ktvu5txjKHOUGLs+ACBwzKhRUfo7OJmpxxIJs26UWKSiNrOpkh6QVC1pjbvfE2sqoMTyLnTKHDHKWdRmVi1ptaQpktokvWhmj7n7rrjDAaGLWuiSPnZgsy8fO+CZibKvSFFm1J+T9Gt33yNJZvZjSVdKoqiBGPRb/hHLvj9dp+f3xl70cEUp6rMk7ct43ibp870Hmdk8SfPST4+Y2e4TzFQv6cAJfm2xkLEwyFgYZCyMUmf8s75eKNjBRHdvktR0st/HzFrcPVmASLEhY2GQsTDIWBghZ4yyPe8tSaMynjekPwcAKIIoRf2ipHPMbLSZDZE0S9Jj8cYCAHTJufTh7h+Z2QJJP1dqe9733f3VGDOd9PJJEZCxMMhYGGQsjGAzmruXOgMAoB+cQg4AgaOoASBwJStqM5tqZrvN7NdmtjjL639iZuvTr28zs8bA8l1kZjvM7CMz+3Ixs+WR8R/MbJeZvWJmvzCzPvdpljDj35vZTjNrNbNnzGxsaBkzxn3JzNzMir6FK8L7OMfMOtLvY6uZ3RBaxvSYq9N/Jl81sx+GltHMVma8h2+Y2eFiZ8zK3Yv+odRByTclfUrSEEkvSxrba8w3JD2YfjxL0vrA8jVKukDSI5K+HOh7+EVJp6Qfzy/me5hHxuEZj6dLejK0jOlxtZJ+Kel5ScnQMkqaI2lVsf8c5pnxHEkvSTot/fxPQ8vYa/xNSm2eKMl7mvlRqhl192np7v6hpK7T0jNdKenh9OMNkiabmYWSz933uvsrkv5YpEy9Rcm4xd3fTz99Xqk98KFlfDfj6TBJxT66HeXPoiR9R9K9kjqLGS4tasZSipLx7yStdvdDkuTu7QFmzDRb0smfs18ApSrqbKeln9XXGHf/SNL/SRpRlHTR8pVavhm/JinCJd4KKlJGM7vRzN6U9E+Sbi5Sti45M5rZZyWNcvcnihksQ9Tf6y+ll7k2mNmoLK/HKUrGT0v6tJn9t5k9n74qZzFF/juTXiYcLWlztteLjYOJFcDMrpOUlLSi1FmycffV7v7nkv5R0m2lzpPJzKok3S/pm6XOksN/Smp09wskPa3j/zcakkFKLX9crNRs9d/MrK6UgfoxS9IGdz9W6iBS6Yo6ymnp3WPMbJCkT0g6WJR0A+O0+UgZzexSSd+SNN3d/1CkbF3yfR9/LGlGnIGyyJWxVtJ5kraa2V5JX5D0WJEPKOZ8H939YMbv7xpJf1mkbF2i/F63SXrM3Y+6+28kvaFUcRdLPn8eZymQZQ9JJTuYOEjSHqX+16JrUf/cXmNuVM+DiT8JKV/G2B+oNAcTo7yH45U6eHJOwL/P52Q8vkJSS2gZe43fquIfTIzyPp6Z8XimpOcDzDhV0sPpx/VKLUOMCCljetxnJO1V+oTAED5K94Oly5X6F/VNSd9Kf265UjM/SaqR9FNJv5b0gqRPBZbvr5SaIbyn1Ez/1QDfw02S3pHUmv54LMCMD0h6NZ1vS38lWaqMvcYWvagjvo93p9/Hl9Pv42cCzGhKLSPtkrRT0qzQMqaff1vSPcXO1t8Hp5ADQOA4mAgAgaOoASBwFDUABI6iBoDAUdQAEDiKGgACV7C7kAOhMbOHlDrpp8sZkoa4++kligScEPZRoyKY2WhJ/yXpG+7OzZkxoLD0gbJnZvWSnpT0HUoaAxEzapQ1MztF0i8kbXL320udBzgRFDXKlplVS9oo6aC7z+1jzGVK3Wnk34saDsgDBxNRzv5F0mCl7izSzcyGKHVxoHclfV6pKzUCwaKoUZbM7A6lrsl8safuEJRpvlKX23zRzJ6RtLvoAYE8cDARZSd9x/pvK3Xrtmcy7iq9Pj1kvKSdZlYr6YCz/ofAMaNG2XH3vUpd+7gvP5f0oKT3lbo2MRA0DiYCQOBY+gCAwFHUABA4ihoAAkdRA0DgKGoACBxFDQCBo6gBIHAUNQAEjqIGgMD9P5gLiaWCWP5lAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 10 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "compare_marginals(state.vae, get_batcher(valid_loader, args), args, cols=5, num_samples=num_samples)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Posterior and Prior Samples"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 1000
    },
    "id": "kcNTB64xhrYx",
    "outputId": "94a41323-768c-4bac-cddd-1e728ab474c4",
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x720 with 15 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x720 with 15 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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Ti6QXS7pp7Pblki7vav/VPrdKunvs9n5Jm6vrmyXt77I91X5vkHRuDm0hy+XLkjzLypMsy8mSPPPPssspvDMkPTR2++FqW582RcTB6vojkjZ1uXPbWyWdJemOvtuSiCwnDDhLiTx/yIDzJMsJA85SIs9j5JYli8grMSpjOzsk0fZGSR+VdElEfKPPtpSGLMtCnuUgy7J0+RrmmGWXBdSXJW0Zu/2salufHrW9WZKqn4e62KntDRq9Ea6NiOv7bMucyLJSQJYSeR5VQJ5kWSkgS4k8Ve0nyyy7LKDulLTN9nNtnyTpdZL2dLj/49kjaWd1fadGc6utsm1JV0m6LyKu6LMtCyBLFZOlRJ6SismTLFVMlhJ55p1lx4u/zpf0BUlflPQbHe/7OkkHJT2h0TzyLklP12j1/v2SPiHptA7acY5GQ42fk3RXdTm/j7aQJVmSZ3l5kmU5WZJn3llyJnIAAIBELCIHAABIRAEFAACQiAIKAAAgEQUUAABAIgooAACARBRQAAAAiSigAAAAElFAAQAAJKKAAgAASEQBBQAAkIgCCgAAIBEFFAAAQCIKKAAAgEQUUAAAAIkooAAAABJRQAEAACSigAIAAEhEAQUAAJCIAgoAACARBRQAAEAiCigAAIBEFFAAAACJKKAAAAASUUABAAAkooACAABIRAEFAACQiAIKAAAgEQUUAABAIgooAACARBRQAAAAiSigAAAAElFAAQAAJKKAAgAASEQBBQAAkIgCCgAAIBEFFAAAQCIKKAAAgEQUUAAAAIkooAAAABJRQAEAACSigAIAAEhEAQUAAJCIAgoAACARBRQAAEAiCigAAIBEFFAAAACJKKAAAAASUUABAAAkooACAABIRAEFAACQiAIKAAAgEQUUAABAIgooAACARBRQAAAAiSigAAAAElFAAQAAJKKAAgAASEQBBQAAkIgCCgAAIBEFFAAAQCIKKAAAgEQUUHOyfb7tXbZPsf0Z29+y/fzqvi2239t3G1HPWJZn277d9m22r7O9gSyHZyzPTbb/yvYnbf+l7c3kOSxHshy7vcP2WnWdLAdmrG9utb1m+9bqsjLEPCmg5vcrkq6V9G1Jr5H0kSN3RMRDkp5p+2n9NA2JjmT5kKSfjoiXSTog6QKyHKQjeR6WdE5EvFzSByTtIs/BOZKlbJ8g6Rc16qd8zg7T0TwlfTIiXlFd1oaYJwVUxfZ/tX1Jzcc+TdIJEfHdiHgiItaO87BPSfrZsd/5jO1/1khjMdMCWR6MiO9Udz0u6fvVdbLs0QJ5fi8ijmR4sqR7quvk2ZN5s6w27ZD0p/pBv5TIslcL5vkS25+y/U7brrYNKk8KKEm2VyS9SdIf1fyVn9BohGKWL0naPnb79yT9l+TGIUkTWdp+jqSfkfRn1Say7Mmiedp+ge07JL1N0merzeTZg0WyrEafXivpQxOPIcueLNg3D0r6cUkvk/QMST9fbR9UnhRQI2+WdOPY6EMb9kj6l7af2eI+sGCWtp8q6U8kvTkinpjyMLLszpu1QJ4RcVdEvFDS2yVdPuVh5NmNN2v+LN8g6cNjI4rTkGV33qw584yIf4iIxyIiJF0v6aemPDTrPJemgLL9+mqB8IdsH7T9kO1XV3e/WtInJx7/btsfG7v9Htt7bZ8k6QuStq6zyx+TdN+RG9Ww5V9rbHgS82krS9snSvqgpN+KiP1jT0GWLWoxz5PGfu3rGq1XlMizNS1+zm6X9CbbH5e0zfb7qu1k2aIW++bJY7/2UkkPVNeHlWdELMVF0rskfUejocIfkfQfJD1Y3bcm6V9MPP7pGn3oniXpLZI+L+mUsfv3SHpKdf1GSV+RdLtGIxeSdJ2kUyee832Sruj7tRj6pa0sJb1R0lcl3VpdfoksB53n2ZJuk3SLpL+QtJk8h5nlxO/sG7tOlgPMU6Pi6681WvP0AUknDjHPE7U8zpT03oi4XpJsf0DSe2w/RdLTJH1z/MER8dXqkMprJJ2i0dE8Xx97yB9Jer2kqyLi/PHftb1F0qMR8XcTbfimpM3N/ZOWVitZRsRVGk3fHUWWnWgzz5eN/y55tq61z9mx31mtnpss29dm3/yL8d8dYp7LVkC9fez2MyR9KyK+a/vvNDpKZ9LfSPpNjQJ/aPyOiPjzaTuqHnvJce46WdLfpzUbx0GWZSHPcpBlWchzhqVYA1UdPrlFoyHHI35BP6iAP6fREQLjv3OmpPdrVEn/ckNN+UlJf9vQcy0lsiwLeZaDLMtCnjX0PYfYxUWjRWpPSvo1jUbdXiPpkKTt1f3/XtKVY48/Q6PDLf+VpH8i6VFJr1iwDU+R9DVJP9r36zHkC1mWdSHPci5kWdaFPNe/LMsU3pkanf30xZL+TtJ+SRdGxL3V/R+QdJftfyxpg0aLwq+IiD3S6EgCSb8j6SULtOHnJN0aEV9Z4DlAlqUhz3KQZVnIcx2uqryi2X6/pC9ExNTv2bH9TkmHIuL3W2rDHRp9lcTdbTz/siDLspBnOciyLOS5vmUpoD4t6bcj4uN9twWLIcuykGc5yLIs5Lm+pVhELun5kv5P341AI8iyLORZDrIsC3muYylGoAAAAJq0LCNQAAAAjVmogLJ9nu39th+wfVlTjUI/yLMcZFkW8iwHWZZj7ik82ydo9OWA50p6WNKdknaMHeKIASHPcpBlWcizHGRZlkXOA3W2pAci4kuSZPuDki6QNPWNcPrpp8fWrVsX2CUWceDAAR0+fNhT7k7Kkyz71WSWEnn2jb5ZDvpmWWbluUgBdYak8e+5eVjSCycfZPsiSRdJ0rOf/Wzt27dvgV1iEaurq7PuXjdPsszHollK5JkT+mY56JtlmZVn64vII+LKiFiNiNWVlZW2d4cWkWVZyLMcZFkW8hyGRQqoL2v0RYNHPKvahmEiz3KQZVnIsxxkWZBFCqg7JW2z/VzbJ0l6naQ9zTQLPSDPcpBlWcizHGRZkLnXQEXEk7bfJukmSSdIujoi7mmsZegUeZaDLMtCnuUgy7IssohcEXGjRt/AjAKQZznIsizkOWIfezDUEL9JgyzLwZnIAQAAElFAAQAAJFpoCg8AgDZNTtsBuWAECgAAIBEFFAAAQCIKKAAAgESsgQIA9GredU7jvzfEUxqgvhyzZgQKAAAgEQUUAABAIqbwEqScBTfH4cZlMO9UwHhGs3Iu4UzIQG5m9bFpj8P86r7GXX/ezfq7mWP2jEABAAAkooACAABIRAEFAACQaGnWQKWsa5n3OefZN+pp+uscJjOY9fysZwMWV7cP08fmk/J3hjVnzWAECgAAIBEFFAAAQKKip/DqTsu0YdYQKUOm6doecq57SgqyGwami7BsZi1LSFmykKscl1IwAgUAAJCIAgoAACARBRQAAECiotdANXGqgmnPNyllnVPd58QPtD1nP7SvEEA7X9sz7XFoF69185r++9e3HN8jjEABAAAkooACAABIVNQUXhND+shT2xnN+/xM1XaL1ztvKZ/BZNSfXF/7oU2vMwIFAACQaN0CyvbVtg/Zvnts22m2b7Z9f/Xz1HabiaaQZznIsizkWQ6yXA51RqB2SzpvYttlkvZGxDZJe6vbGIbdIs9S7BZZlmS3yLMUu0WWxVu3gIqI2yR9bWLzBZKuqa5fI+nCZps1n4g45lL3sbPYPnopwZDynGY8ky5ymdzf+GXyPTft0oYSslxP3axnvd4p75e2M1tn34PMc1Z/WFa5ZTmZS65/1+p+tuZi3jVQmyLiYHX9EUmbGmoP+kGe5SDLspBnOciyMAsvIo9ROTi1JLR9ke19tvetra0tuju0bFaeZDks9M2y0DfLQd8sw7wF1KO2N0tS9fPQtAdGxJURsRoRqysrK3PubnHzDgFOG/acd1ogp+HHMbXyzCXLSbNymWeouuspwoYNrm+maGJIf1a2GeaeXd+ct3/k9DnYU85Z9s0mPjOb0sTf2y7NW0DtkbSzur5T0g3NNAc9Ic9ykGVZyLMcZFmYOqcxuE7S7ZKeZ/th27skvUvSubbvl/Sq6jYGgDzLQZZlIc9ykOVyWPdM5BGxY8pdr2y4LegAeZaDLMtCnuUgy+VQ1Fe5TGri6znmfY5Zv9f3/P/QHe8w9VQ5zaPjWLOymdY3ybM/s3Lo8rNu3vfAeqfHWDa5/Jub+JxvG1/lAgAAkIgCCgAAIFHRU3h11Z0yaOo5cxkiLUXdqZwmhoDJLh85DumXqu1+Ne++2+6PfU5JNmnWvyPXfpTynusrF0agAAAAElFAAQAAJFqaKbxchynRrLpDuUyx5quJ6YW6z0HWi+tzOqju/po6oquJI7T7kPLv7/PfOLS/04xAAQAAJKKAAgAASEQBBQAAkGhp1kA1YdZ8cMrc7VDn0YdoWi5DOMstflgTa9zQrCY+z+ZdyzTrOep+GwTvlWbM8zpOZjRvLn39TWUECgAAIBEFFAAAQKKipvDmPTtp3WHhWc8/75RQLmdULUUTw/Fkko8mXnvyy1/Tp65oqy3L8F5qe3qzpOlTRqAAAAASUUABAAAkooACAABIVNQaqLqHrUrtn8q+qVMeYH2z8qqbZUnz8suIzPIwa81QE6cq6MKyn2am7lcfNfF1OLOeP+X3+sIIFAAAQCIKKAAAgERFTeGlSJnu69KyDx/Po+5hx/O+tmSSpxyH9EvVxmkGpvWread4JtWd2p+1j1JPY9DGGb/r5lnStwkwAgUAAJCIAgoAACARBRQAAECipV0D1aWUudxS5ti71Pbh0cuwJqI05NKdWf2j6UPi2zgEPtf1sF1Jed3mea26OBVQXzmtOwJle4vtW2zfa/se2xdX20+zfbPt+6ufp7bfXCzi8ccfF1mWg75ZDvpmWeiby6HOFN6Tki6NiO2SXiTprba3S7pM0t6I2CZpb3UbGauqdrIsB32zEPTN4tA3l8C6BVREHIyIz1bXvynpPklnSLpA0jXVw66RdGFLbZyb7aOXXPcdEcdc2rRhwwYNNcs+9fk+mmXIfbNpXfajNgypb6a81rMe13S/Gn++403xTLu0oZS+OZR+NZl9V5/ZSYvIbW+VdJakOyRtioiD1V2PSNrUbNPQJrIsC3mWgyzLQp7lql1A2d4o6aOSLomIb4zfF6PS9Ljlqe2LbO+zvW9tbW2hxqIZZFkW8iwHWZaFPMtWq4CyvUGjN8G1EXF9tflR25ur+zdLOnS8342IKyNiNSJWV1ZWmmgzFkCWZSHPcpBlWcizfHWOwrOkqyTdFxFXjN21R9LO6vpOSTc037z1DWGdUy6qOexssxyCnNYE5N432zC0PldXKX1zVv+Ydx3SrMfNes4+++ky9s0u9Z3vEXXOA/USSW+U9Hnbd1Xbfl3SuyR92PYuSQ9Kem0rLURjHnvsMYksS0LfLAR9szj0zSWwbgEVEZ+WNO2/e69stjlo08aNGxURZFkI+mY56JtloW8uh8GfiXzW8N34fcc7rDX1vln7Km1KoRTTcul7+g3T1e1LZFiOulmSOaS0v+d1f28efBceAABAIgooAACARBRQAAAAiQa/BmpeKfOk07bXXUeFdtWd/x6XsmaNLAEgH5OfyXXXKjf9Wc4IFAAAQCIKKAAAgERLO4U3z7TPpLrDhsgf+Q0DOQHIBSNQAAAAiSigAAAAElFAAQAAJFqaNVBdHtqI/pDl8KSsQWTdIYBJfX0WMAIFAACQiAIKAAAg0dJM4QHIE1NxAIaIESgAAIBEFFAAAACJKKAAAAASUUABAAAkooACAABIRAEFAACQyF0eQmx7TdKDkk6XdLizHU+3bO14TkSsNPFEZDlTF21pLEvpaJ6Pablewzrom4vLpR0SfbMJueTZe9/stIA6ulN7X0Ssdr5j2tG4XNqeSzukvNqSIqd259KWXNoxj1zanks7pLzakiKndufSlhzawRQeAABAIgooAACARH0VUFf2tN9JtGNxubQ9l3ZIebUlRU7tzqUtubRjHrm0PZd2SHm1JUVO7c6lLb23o5c1UAAAAEPGFB4AAECiTgso2+fZ3m/7AduXdbzvq20fsn332LbTbN9s+/7q56kdtGOL7Vts32v7HtsX99WWRZBlOVlK5Fnts4g8ybKcLCXyzDnLzgoo2ydI+kNJr5a0XdIO29u72r+k3ZLOm9h2maS9EbFN0t7qdtuelHRpRGyX9CJJb61ehz7aMheyPGrwWUrkOWbweZLlUYPPUiLPSr5ZRkQnF0kvlnTT2O3LJV3e1f6rfW6VdPfY7f2SNlfXN0va32V7qv3eIOncHNpClsuXJXmWlSdZlpMleeafZZdTeGdIemjs9sPVtj5tioiD1fVHJG3qcue2t0o6S9IdfbclEVlOGHCWEnn+kAHnSZYTBpylRJ7HyC1LFpFXYlTGdnZIou2Nkj4q6ZKI+EafbSkNWZaFPMtBlmXp8jXMMcsuC6gvS9oydvtZ1bY+PWp7syRVPw91sVPbGzR6I1wbEdf32ZY5kWWlgCwl8jyqgDzJslJAlhJ5qtpPlll2WUDdKWmb7efaPknS6yTt6XD/x7NH0s7q+k6N5lZbZduSrpJ0X0Rc0WdbFkCWKiZLiTwlFZMnWaqYLCXyzDvLjhd/nS/pC5K+KOk3Ot73dZIOSnpCo3nkXZKertHq/fslfULSaR204xyNhho/J+mu6nJ+H20hS7Ikz/LyJMtysiTPvLPkTOQAAACJWEQOAACQiAIKAAAgEQUUAABAIgooAACARBRQAAAAiSigAAAAElFAAQAAJKKAAgAASEQBBQAAkIgCCgAAIBEFFAAAQCIKKAAAgEQUUAAAAIkooAAAABJRQAEAACSigAIAAEhEAQUAAJCIAgoAACARBRQAAEAiCigAAIBEFFAAAACJKKAAAAASUUABAAAkooACAABIRAEFAACQiAIKAAAgEQUUAABAIgooAACARBRQAAAAiSigAAAAElFAAQAAJKKAAgAASEQBBQAAkIgCCgAAIBEFFAAAQCIKKAAAgEQUUAAAAIkooAAAABJRQAEAACSigAIAAEhEAQUAAJCIAgoAACARBRQAAEAiCigAAIBEFFAAAACJKKAAAAASUUABAAAkooACAABIRAEFAACQiAIKAAAgEQUUAABAIgooAACARBRQAAAAiSigAAAAElFAAQAAJKKAAgAASEQBBQAAkIgCCgAAIBEFFAAAQCIKKAAAgEQUUAAAAIkooDpi+3zbu6rrp9j+jO1v2X5+tW2L7ff220rUNZHn2bZvt32b7etsbyDP4ZjIcpPtv7L9Sdt/aXszWQ7LeJ5j23bYXquuk+dATPTNrbbXbN9aXVb6zpICqju/Iuna6vq3Jb1G0keO3BkRD0l6pu2ndd80zGE8z4ck/XREvEzSAUkXkOegjGd5WNI5EfFySR+QtIssB2c8T9k+QdIvatRP+awdlmOylPTJiHhFdVnrO0sKqAXYfoftd9R43NMknRAR35WkiHgiItaO89BPSfrZRhuJ2hbI82BEfKe6+3FJ36+uk2dPFsjyexFxJL+TJd1TXSfLHs2bZ2WHpD/VD/qlRJ69WTDLl9j+lO132na1rbcsB19A2d5o+4Dt149tO9n2/7P9C8d5/P+w/d8ntr3c9ldtbz7O4w/Y/k413Xbk8qOJzfwJjUYm1vMlSdsTn7soQ87T9nMk/YykP6s2LXWeQ83S9gts3yHpbZI+W21e6iylYeZZjT69VtKHJh631HkOMUtJByX9uKSXSXqGpJ+vtveW5eALqIj4lkbDfL9ve6Xa/G5J+yLiI8f5lYslvdr2uZJk+ymS/ljSpRFxcMpufi4iNo5dvtLwPwOVoeZp+6mS/kTSmyPiiUWfrwRDzTIi7oqIF0p6u6TLF32+Ugw0zzdI+vDYqCI0zCwj4h8i4rGICEnXS/qpRZ6vCYMvoCQpIm6S9OeS3mf7FRr9j+NXpzz2q5L+raQrbf9TSb8p6YsRsXvRdth+t+2Pjd1+j+29GlXRW2s8xY9Jum/Rdgzd0PK0faKkD0r6rYjYP/YUS5/nALM8aezXvq7RekWJLCUNL0+NRibeZPvjkrbZfl+1fenzHFqWtk8e+7WXSnqgut5flhFRxEXSqRoN8R2W9K9rPP6jkvZI+qqkLTMed0DSq6bc9w5J7xi7/XSNPnTPkvQWSZ+XdEp13x5JTxl77I2SviLpdo1GLSTpOkmn9v1a5nAZUp6S3ljt99bq8kvkOdgsz5Z0m6RbJP2FpM1kOdw8J55j39h18hxYlpJeLemvNVrz9AFJJ/adZe8BNvxm+IRG/2M8pcZjN0n6lqSL13ncgepxf19dPjbtjTC27XOSHhx/g2l01N2uGfvZIun3+34Nc7qQZzkXsizrQp7lXMhy/ksRU3iSZPsNGg33fULS7673+Ih4VKOq+571Hivpwoh4WnW5cJ3H/o2kMyVdHqNDLI/s788j4qoZ7XkoIi6p0ZalQJ7lIMuykGc5yHIxRRRQtp8h6b2S/o1GC+Nea/ulPbTjTEnvl3SNpF/uev+lIM9ykGVZyLMcZLm4IgooSX+g0RDhLTE6IuA/Sfpj2/9Ikmzvtr27zhOlPHbi987Q6PD1t2i0EO/MamEe0pFnOciyLORZDrJc0OALKNsXSjpH0n88si0i/ptGC7T/c7Vpi6T/XfMpUx57pA1P1WhR+BURsScivi3pPZJ+J+V5QJ4lIcuykGc5yLIZrhZiFas6LPlvJf3zWOf8PCmPrR7/DkmKiHcs3lLUQZ7lIMuykGc5yLKeE/tuQNsi4nFJP9n0Y9EP8iwHWZaFPMtBlvUUX0C17Na+G4BG3dp3A9CYW/tuABp1a98NQGNu7bsBTSl+Cg8AAKBpg19EDgAA0LWFCijb59neb/sB25c11Sj0gzzLQZZlIc9ykGU55p7Cs32CpC9IOlfSw5LulLQjIu5trnnoCnmWgyzLQp7lIMuyLLKI/GxJD0TElyTJ9gclXSBp6hvh9NNPj61bty6wSyziwIEDOnz4sKfcnZQnWfarySwl8uwbfbMc9M2yzMpzkQLqDEkPjd1+WNILJx9k+yJJF0nSs5/9bO3bt2+BXWIRq6urs+5eN0+yzMeiWUrkmRP6Zjnom2WZlWfri8gj4sqIWI2I1ZWVlbZ3hxaRZVnIsxxkWRbyHIZFCqgva3T69iOeVW3DMJFnOciyLORZDrIsyCIF1J2Sttl+bnUq99dJ2tNMs9AD8iwHWZaFPMtBlgWZew1URDxp+22SbpJ0gqSrI+KexlqGTpFnOciyLORZDrIsy0Jf5RIRN2r0bcooAHmWgyzLQp4j9rEHQw3xmzTIshyciRwAACARBRQAAECihabwAABo0+S0HZALRqAAAAASUUABAAAkooACAABIxBooAECv5l3nNP57QzylAerLMWtGoAAAABJRQAEAACRiCi9ByllwcxxuXAbzTgWMZzQr5xLOhAzkZlYfm/Y4zK/ua9z1592sv5s5Zs8IFAAAQCIKKAAAgEQUUAAAAImWZg1UyrqWeZ9znn2jnqa/zmEyg1nPz3o2YHF1+zB9bD4pf2dYc9YMRqAAAAASUUABAAAkKnoKr+60TBtmDZEyZJqu7SHnuqekILthYLoIy2bWsoSUJQu5ynEpBSNQAAAAiSigAAAAElFAAQAAJCp6DVQTpyqY9nyTUtY51X1O/EDbc/ZD+woBtPO1PdMeh3bxWjev6b9/fcvxPcIIFAAAQCIKKAAAgERFTeE1MaSPPLWd0bzPz1Rtt3i985byGUxG/cn1tR/a9DojUAAAAInWLaBsX237kO27x7adZvtm2/dXP09tt5loCnmWgyzLQp7lIMvlUGcEarek8ya2XSZpb0Rsk7S3uo1h2C3yLMVukWVJdos8S7FbZFm8dQuoiLhN0tcmNl8g6Zrq+jWSLmy2WfOJiGMudR87i+2jlxIMKc9pxjPpIpfJ/Y1fJt9z0y5tKCHL9dTNetbrnfJ+aTuzdfY9yDxn9YdllVuWk7nk+net7mdrLuZdA7UpIg5W1x+RtKmh9qAf5FkOsiwLeZaDLAuz8CLyGJWDU0tC2xfZ3md739ra2qK7Q8tm5UmWw0LfLAt9sxz0zTLMW0A9anuzJFU/D017YERcGRGrEbG6srIy5+4WN+8Q4LRhz3mnBXIafhxTK89cspw0K5d5hqq7niJs2OD6ZoomhvRnZZth7tn1zXn7R06fgz3lnGXfbOIzsylN/L3t0rwF1B5JO6vrOyXd0Exz0BPyLAdZloU8y0GWhalzGoPrJN0u6Xm2H7a9S9K7JJ1r+35Jr6puYwDIsxxkWRbyLAdZLod1z0QeETum3PXKhtuCDpBnOciyLORZDrJcDkV9lcukJr6eY97nmPV7fc//D93xDlNPldM8Oo41K5tpfZM8+zMrhy4/6+Z9D6x3eoxlk8u/uYnP+bbxVS4AAACJKKAAAAASFT2FV1fdKYOmnjOXIdJS1J3KaWIImOzykeOQfqna7lfz7rvt/tjnlGSTZv07cu1HKe+5vnJhBAoAACARBRQAAECipZnCy3WYEs2qO5TLFGu+mpheqPscZL24PqeD6u6vqSO6mjhCuw8p//4+/41D+zvNCBQAAEAiCigAAIBEFFAAAACJlmYNVBNmzQenzN0OdR59iKblMoSz3OKHNbHGDc1q4vNs3rVMs56j7rdB8F5pxjyv42RG8+bS199URqAAAAASUUABAAAkKmoKb96zk9YdFp71/PNOCeVyRtVSNDEcTyb5aOK1J7/8NX3qirbasgzvpbanN0uaPmUECgAAIBEFFAAAQCIKKAAAgERFrYGqe9iq1P6p7Js65QHWNyuvulmWNC+/jMgsD7PWDDVxqoIuLPtpZup+9VETX4cz6/lTfq8vjEABAAAkooACAABIVNQUXoqU6b4uLfvw8TzqHnY872tLJnnKcUi/VG2cZmBav5p3imdS3an9Wfso9TQGbZzxu26eJX2bACNQAAAAiSigAAAAElFAAQAAJFraNVBdSpnLLWWOvUttHx69DGsiSkMu3ZnVP5o+JL6NQ+BzXQ/blZTXbZ7XqotTAfWV07ojULa32L7F9r2277F9cbX9NNs3276/+nlq+83FIh5//HGRZTnom+Wgb5aFvrkc6kzhPSnp0ojYLulFkt5qe7ukyyTtjYhtkvZWt5Gxqmony3LQNwtB3ywOfXMJrFtARcTBiPhsdf2bku6TdIakCyRdUz3sGkkXttTGudk+esl13xFxzKVNGzZs0FCz7FOf76NZhtw3m9ZlP2rDkPpmyms963FN96vx5zveFM+0SxtK6ZtD6VeT2Xf1mZ20iNz2VklnSbpD0qaIOFjd9YikTc02DW0iy7KQZznIsizkWa7aBZTtjZI+KumSiPjG+H0xKk2PW57avsj2Ptv71tbWFmosmkGWZSHPcpBlWcizbLUKKNsbNHoTXBsR11ebH7W9ubp/s6RDx/vdiLgyIlYjYnVlZaWJNmMBZFkW8iwHWZaFPMtX5yg8S7pK0n0RccXYXXsk7ayu75R0Q/PNW98Q1jnloprDzjbLIchpTUDufbMNQ+tzdZXSN2f1j3nXIc163Kzn7LOfLmPf7FLf+R5R5zxQL5H0Rkmft31Xte3XJb1L0odt75L0oKTXttJCNOaxxx6TyLIk9M1C0DeLQ99cAusWUBHxaUnT/rv3ymabgzZt3LhREUGWhaBvloO+WRb65nIY/JnIZw3fjd93vMNaU++bta/SphRKMS2XvqffMF3dvkSG5aibJZlDSvt7Xvf35sF34QEAACSigAIAAEhEAQUAAJBo8Gug5pUyTzpte911VGhX3fnvcSlr1sgSAPIx+Zlcd61y05/ljEABAAAkooACAABItLRTePNM+0yqO2yI/JHfMJATgFwwAgUAAJCIAgoAACARBRQAAECipVkD1eWhjegPWQ5PyhpE1h0CmNTXZwEjUAAAAIkooAAAABItzRQegDwxFQdgiBiBAgAASEQBBQAAkIgCCgAAIBEFFAAAQCIKKAAAgEQUUAAAAInc5SHEttckPSjpdEmHO9vxdMvWjudExEoTT0SWM3XRlsaylI7m+ZiW6zWsg765uFzaIdE3m5BLnr33zU4LqKM7tfdFxGrnO6Ydjcul7bm0Q8qrLSlyancubcmlHfPIpe25tEPKqy0pcmp3Lm3JoR1M4QEAACSigAIAAEjUVwF1ZU/7nUQ7FpdL23Nph5RXW1Lk1O5c2pJLO+aRS9tzaYeUV1tS5NTuXNrSezt6WQMFAAAwZEzhAQAAJOq0gLJ9nu39th+wfVnH+77a9iHbd49tO832zbbvr36e2kE7tti+xfa9tu+xfXFfbVkEWZaTpUSe1T6LyJMsy8lSIs+cs+ysgLJ9gqQ/lPRqSdsl7bC9vav9S9ot6byJbZdJ2hsR2yTtrW637UlJl0bEdkkvkvTW6nXooy1zIcujBp+lRJ5jBp8nWR41+Cwl8qzkm2VEdHKR9GJJN43dvlzS5V3tv9rnVkl3j93eL2lzdX2zpP1dtqfa7w2Szs2hLWS5fFmSZ1l5kmU5WZJn/ll2OYV3hqSHxm4/XG3r06aIOFhdf0TSpi53bnurpLMk3dF3WxKR5YQBZymR5w8ZcJ5kOWHAWUrkeYzcsmQReSVGZWxnhyTa3ijpo5IuiYhv9NmW0pBlWcizHGRZli5fwxyz7LKA+rKkLWO3n1Vt69OjtjdLUvXzUBc7tb1BozfCtRFxfZ9tmRNZVgrIUiLPowrIkywrBWQpkaeq/WSZZZcF1J2Sttl+ru2TJL1O0p4O9388eyTtrK7v1GhutVW2LekqSfdFxBV9tmUBZKlispTIU1IxeZKlislSIs+8s+x48df5kr4g6YuSfqPjfV8n6aCkJzSaR94l6ekard6/X9InJJ3WQTvO0Wio8XOS7qou5/fRFrIkS/IsL0+yLCdL8sw7S85EDgAAkIhF5AAAAIkooAAAABJRQAEAACSigAIAAEhEAQUAAJCIAgoAACARBRQAAEAiCigAAIBE/x8AuKz5b3EtQQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 720x720 with 15 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "compare_samples(state.vae, get_batcher(valid_loader, args), args, N=5, num_figs=3, num_samples=100, \n",
    "                filename=plots_dir / 'posterior-grid')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## TSNE"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "id": "dpY7GkEQhrYx"
   },
   "outputs": [],
   "source": [
    "from analysis import samples_per_digit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "id": "OSgvWiwy86Is"
   },
   "outputs": [],
   "source": [
    "f, y, z, x, marginal_f, scores, concs = samples_per_digit(\n",
    "    state.vae, get_batcher(valid_loader, args, onehot=False), \n",
    "    args, return_marginal=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((10, 458, 0), (10, 0), (10, 458, 10), (10, 10), (10, 458, 784), (10, 784))"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f.shape, f.mean(1).shape, z.shape, z.mean(1).shape, x.shape, x.mean(1).shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((10, 458, 0), (10, 0), (10, 458, 0), (10, 0), (10, 458, 0), (10, 0))"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "marginal_f.shape, marginal_f.mean(1).shape, scores.shape, scores.mean(1).shape, concs.shape, concs.mean(1).shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's appreciate the sparsity of the samples"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.manifold import TSNE"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's appreciate structure in latent space"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [],
   "source": [
    "def tsne_plot(samples, title, legend=True, filename=None):\n",
    "    \"\"\"\n",
    "    :param samples: [10, N,D]\n",
    "    \"\"\"\n",
    "    assert samples.shape[0] == 10, \"I need 10 digits\"\n",
    "    D = samples.shape[-1]\n",
    "    assert D > 0, \"0-dimensional features?\"\n",
    "    tsne_results = TSNE(n_components=2, random_state=1).fit_transform(samples.reshape(-1, D)).reshape(10, -1, 2)\n",
    "    plt.figure(figsize=(6, 5))\n",
    "    colors = 'r', 'g', 'b', 'c', 'm', 'y', 'k', 'gray', 'orange', 'purple'\n",
    "    for i, c in zip(np.arange(10), colors):\n",
    "        plt.scatter(tsne_results[i, :, 0], tsne_results[i, :, 1], c=c, label=i)\n",
    "    plt.xticks([], [])    \n",
    "    plt.yticks([], [])\n",
    "    if legend:\n",
    "        #plt.legend(bbox_to_anchor=(1, 0.85), loc='upper left', framealpha=0.5)\n",
    "        plt.legend(loc='lower right', framealpha=1.0, ncol=2, fontsize='small')\n",
    "    #plt.title(title)\n",
    "    \n",
    "    if filename:\n",
    "        plt.savefig(f'{filename}.pdf', bbox_inches='tight') \n",
    "    plt.show()\n",
    "\n",
    "    return tsne_results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "if state.vae.p.z_dim:\n",
    "    _ = tsne_plot(z, r\"$Z|X_{obs}$\", filename=plots_dir / 'tsne-z')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "if state.vae.p.z_dim:\n",
    "    _ = plt.hist((z > 0.).sum(-1).flatten(), label=\"0\")\n",
    "    _ = plt.hist((z > 0.01).sum(-1).flatten(), label=\"0.01\")\n",
    "    _ = plt.hist((z > 0.1).sum(-1).flatten(), label=\"0.1\")\n",
    "    _ = plt.hist((z > 0.25).sum(-1).flatten(), label=\"0.25\")\n",
    "    _ = plt.hist((z > 0.5).sum(-1).flatten(), label=\"0.5\")    \n",
    "    _ = plt.legend()\n",
    "    plt.savefig(plots_dir / 'threshold-z.pdf', bbox_inches='tight')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Marginal samples per class"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 10 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "marginal_x = x.mean(1)\n",
    "fig, axs = plt.subplots(\n",
    "    2, 5, \n",
    "    sharex=True, sharey=True,\n",
    "    gridspec_kw={'hspace': 0, 'wspace': 0})\n",
    "for c in range(10):\n",
    "    axs[c // 5, c % 5].imshow(marginal_x[c].reshape(args.height, args.width), cmap='Greys')\n",
    "for ax in axs.flat:\n",
    "    ax.set_xticks([])\n",
    "    ax.set_yticks([])\n",
    "# Hide x labels and tick labels for top plots and y ticks for right plots.\n",
    "for ax in axs.flat:\n",
    "    ax.label_outer()\n",
    "fig.savefig(plots_dir / 'posterior-marginal-samples.pdf', bbox_inches='tight')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Samples from Corner"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As the Dirichlet does not include the vertices of the simplex, we need to poke onehot vectors inside of it, which we do by adding some small random noise."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [],
   "source": [
    "def probe_corners(vae, batcher, args, num_samples=None, plus_eps=0.1): \n",
    "    if num_samples is None:\n",
    "        num_samples = args.num_samples\n",
    "\n",
    "    with torch.no_grad():\n",
    "        vae.eval()        \n",
    "    \n",
    "        samples = [defaultdict(list) for _ in range(vae.p.z_dim)]\n",
    "\n",
    "        for i in range(vae.p.z_dim):\n",
    "            z = torch.zeros(vae.p.z_dim, device=torch.device(args.device))\n",
    "            z[i] = 1.0\n",
    "            z += td.Uniform(0., plus_eps).sample(z.shape).to(torch.device(args.device))\n",
    "            z /= z.sum(-1, keepdims=True)\n",
    "            z = z.expand((num_samples, vae.p.z_dim))\n",
    "            \n",
    "            f = vae.p.F().expand((num_samples,)).sample()\n",
    "            y = vae.p.Y(f).sample()\n",
    "            \n",
    "            # [S, K]\n",
    "            x = vae.p.X(z=z, y=y).sample()\n",
    "                        \n",
    "            # [B, K]\n",
    "            samples[i]['y'] = y.cpu().numpy()\n",
    "            samples[i]['z'] = z.cpu().numpy()\n",
    "            samples[i]['x'] = x.cpu().numpy()\n",
    "\n",
    "    return samples"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [],
   "source": [
    "corner_samples = probe_corners(state.vae, get_batcher(valid_loader, args), args, num_samples=100, plus_eps=0.1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(100, 784)"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "corner_samples[0]['x'].shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 10 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axs = plt.subplots(\n",
    "    2, 5, \n",
    "    sharex=True, sharey=True,\n",
    "    gridspec_kw={'hspace': 0, 'wspace': 0})\n",
    "for c in range(10):\n",
    "    axs[c // 5, c % 5].imshow(corner_samples[c]['x'].mean(0).reshape(args.height, args.width), cmap='Greys')\n",
    "    #axs[c // 5, c % 5].set_xlabel(c) #set_title(f\"X'|X={c}\")\n",
    "for ax in axs.flat:\n",
    "    ax.set_xticks([])\n",
    "    ax.set_yticks([])\n",
    "# Hide x labels and tick labels for top plots and y ticks for right plots.\n",
    "for ax in axs.flat:\n",
    "    ax.label_outer()\n",
    "#_ = fig.suptitle(r'Samples from vertices')  \n",
    "fig.savefig(plots_dir / 'prior-corner-samples-1e-1.pdf', bbox_inches='tight')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [],
   "source": [
    "corner_samples = probe_corners(state.vae, get_batcher(valid_loader, args), args, num_samples=100, plus_eps=0.01)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 10 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axs = plt.subplots(\n",
    "    2, 5, \n",
    "    sharex=True, sharey=True,\n",
    "    gridspec_kw={'hspace': 0, 'wspace': 0})\n",
    "for c in range(10):\n",
    "    axs[c // 5, c % 5].imshow(corner_samples[c]['x'].mean(0).reshape(args.height, args.width), cmap='Greys')\n",
    "    #axs[c // 5, c % 5].set_xlabel(c) #set_title(f\"X'|X={c}\")\n",
    "for ax in axs.flat:\n",
    "    ax.set_xticks([])\n",
    "    ax.set_yticks([])\n",
    "# Hide x labels and tick labels for top plots and y ticks for right plots.\n",
    "for ax in axs.flat:\n",
    "    ax.label_outer()\n",
    "#_ = fig.suptitle(r'Samples from vertices')  \n",
    "fig.savefig(plots_dir / 'prior-corner-samples-1e-2.pdf', bbox_inches='tight')"
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